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The number of values of x in [0,2pi] sat...

The number of values of `x` in `[0,2pi]` satisfying the equation `|cos x – sin x| >= sqrt2` is

A

0

B

1

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We know that ltBrgt `|"cos" x -"sin"x| le sqrt(2)`
`therefore |"cos" x - "sin"x| ge sqrt(2)`
`rArr |"cos" x - "sin" x| = sqrt(2)`
`rArr "cos" x - "sin" x = sqrt(2), -sqrt(2)`
`rArr "cos" (x+ (pi)/(4)) = 1, -1`
`rArr x + (pi)/(4) = 0, pi 2 pi rArr x = (3pi)/(4), (7pi)/(4) " " [because x in [0, 2pi]`
Hence, there are two values of x.
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  12. If theta(1), theta(2), theta(3), theta(4) are roots of the equation "s...

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